1. Field of the Invention
The invention relates to a Chien search method in Reed-Solomon decoding, more particularly to a Chien search method and system in Reed-Solomon decoding, which can directly find an error symbol location through table lookup so as to enhance efficiency.
2. Description of the Related Art
In recent years, demand for reliable signal transmission with respect to products ranging from consumer electronic products to communications electronic products has increased considerably. Therefore, error detection and correction mechanisms are becoming more and more important. During the process of digital communication, to ensure the accuracy of source data to be transmitted, a transmitting end generally will append redundant data to the source data, so that the receiving end can perform error correction based on the redundant data. The Reed-Solomon code is a widely used correction code. Since the Reed-Solomon code has a good correction capability with respect to errors generated in transmission channels, it has become a very popular channel coding scheme, and is now a widely used error correction code in satellite communication systems, digital television systems, various digital audiovisual recording media, etc.
Even though the Reed-Solomon code has excellent performance in error correction, the amount of computations required for decoding is huge. Consequently, hardware is often used for calculation and processing. If the Reed-Solomon code is executed in a processor in the form of program decoding, the decoding speed will inevitably become extremely slow due to the huge computation amount. Therefore, in some applications of communications devices with software-defined operations (such as software defined radio (SDR)), accelerating the program decoding speed of the Reed-Solomon code has become an important subject of research.
Referring to FIG. 1, an existing Reed-Solomon decoding procedure can be divided into four stages, which are, as shown, a stage 11 of calculating syndromes, a stage 12 of calculating error location polynomials, a stage 13 of executing a Chien search, and a stage 14 of calculating error values. In this Reed-Solomon decoding procedure, about 40% of the computation amount is concentrated on the Chien search at stage 13. If the processing time for executing the Chien search can be effectively reduced, the decoding speed of the Reed-Solomon code can be successfully accelerated.
Referring to FIG. 2, a conventional Chien search method in Reed-Solomon decoding includes the following steps. In step 21, a location index j and a symbol index i are initialized, i.e., j=0, and i=0. In step 22, an error evaluation value Λ(αi) is calculated. In step 23, a decision is performed to determine if the error evaluation value Λ(αi) is equal to 0. If yes, this indicates that an error occurs in a symbol at the ith position, and step 24 is carried out to perform the necessary processing. Otherwise, the flow goes to the processing in step 26. In steps 24 and 25, the current symbol index i is first stored in an error location array, Location[j]=i, followed by incrementing the location index, j=j+1. In steps 26-27, a decision is performed to determine if the Chien search has been completed, i.e., determining if i=n−1. If yes, the Chien search is ended. Otherwise, the symbol index i is incremented, i=i+1, and the aforesaid steps are repeated, in which n represents a total number of symbols of a Reed-Solomon block code that was received. In this conventional method, the finite field multiplication, the finite field addition, and the subsequent comparison and determination processing which are required to calculate the error evaluation value involve very time-consuming computations.
Another conventional Chien search method in Reed-Solomon decoding is disclosed in U.S. Pat. No. 6,263,470, in which a finite field multiplication result required for calculating the error evaluation value Λ(αi) is found from a pre-defined finite field multiplication result table so as to reduce the time required for executing the aforesaid step 22. However, this conventional method merely reduces the time for computing the finite field multiplication. It is still required to perform the finite field addition and the subsequent comparison and determination processing. Thus, there is room for improvement.
Accordingly, there is a need to find a solution such that the time for processing the Chien search can be further reduced, thereby increasing the speed of decoding the Reed-Solomon Code.